$ \left(\dfrac{1}{81}\right)^{-\frac{3}{4}}$
$= 81^{\frac{3}{4}}$ $= \left(81^{\frac{1}{4}}\right)^{3}$ To simplify $81^{\frac{1}{4}}$ , figure out what goes in the blank: $\left(? \right)^{4}=81$ To simplify $81^{\frac{1}{4}}$ , figure out what goes in the blank: $\left({3}\right)^{4}=81$ so $ 81^{\frac{1}{4}}=3$ So $81^{\frac{3}{4}}=\left(81^{\frac{1}{4}}\right)^{3}=3^{3}$ $= 3\cdot3\cdot 3$ $= 9\cdot3$ $= 27$